REGULAR PERMUTATIONS OF QUASIGROUPS

The right or left nuclei of loops are subgroups measuring their nearassociativity. V. D. Belousov generalized these to proper quasigroups by introduction the notions of right and left regular permutations. The aim of this paper is to investigate extensions of quasigroups such that the orbits of the groups of right or left regular permutations are contained in the kernels of the homomorphism associated with the extension.